Adaptive beamformer with time constant control

ABSTRACT

An adaptive beamformer and signal processor for sonar and other signal receptor arrays, in which beamforming is accomplished by correlation feedback loops providing matched weighting across the array. For improved performance of the adaptive beamformer thus comprised in the presence of large input transients, while preserving its steady state performance essentially unchanged, the time constant of the correlation feedback loops is placed under automatic control and adjusted thereby to prevent saturation of the loops even with large interference transients.

United States Patent Hadley et al.

[ ADAPTIVE BEAMFORMER WITH TIME CONSTANT CONTROL Inventors: Hugh W.Hadley, Skaneateles; David W. Saum, Syracuse, both of N.Y.

General Electric Company, Syracuse, N.Y.

Filed: Dec. 10, 1971 Appl. No.: 206,618

[73] Assignee:

US. Cl. 343/100 SA, 343/100 LE Int. Cl. H04b 7/00 Field of Search343/100 SA, 100 LE References Cited UNITED STATES PATENTS 4/1965Saltzberg 343/100 LE OTHER PUBLICATIONS Widrow et al., Proc. of IEEE,Vol. 55, No. 12,

Primary Examiner-Benjamin A. Borchelt Assistant Examiner-S1 C. BuczinskiAttorney-Carl W. Baker et al.

[5 7] ABSTRACT 5 Claims, 3 Drawing Figures BEAM TIME DELAY STEERED T0TARGET J3 (PRIOR ART) BEAM TIME DELAY STEERED TO INTERFERENCE PatentedOct. 2, 1973 3,763,490

T BEAM TIME DELAY 7 STEEREDTO T l7 Pz L WP +P FlG.l n4 Z. (PRIOR ART) 2i T 2 Q4 4 W/I BEAM TIME DELAY STEERED TO INTERFERENCE M t W t iw ty.(t)e y me YNme FIG 2 LAT. 9 :8 i (PRIOR ART) REFERENCE BEAM -A IJNQPERTURBATION BEAM 23 mt 9 /G] \l Y H.) 2| l9 v g REFERENCE BEAM OUTPUTPERTURBA- TION BEAM ADAPTIVE BEAMFORMER WITH TIME CONSTANT CONTROLBACKGROUND OF THE INVENTION The invention herein described was made inthe course of or under a contract with the Department of the Navy.

This invention relates generally to signal detection in systemsutilizing arrayed receptors for acoustic and electromagnetic wavesignals as in sonar, radar, communications and seismic wave detectionsystems. More particularly, the invention relates to the processing ofsignals as received by such receptor arrays to accomplish arraybeamforming and to extract useful signal output from signals whenreceived in company with large interference transients.

Many reports have appeared in recent literature on efforts to achieveoptimal space-time processing of signals in array systems particularlyfor sonar application, so as to maximize system capabilities to detectuseful signals immersed in noise. From these efforts there has evolvedan optimal processor concept which is fairly well defined, and whichalso is narrowly defined in the sense that there is a strong similarityamong most if not all of the so-called optimal processors. Generallysuch processors are composed of a beamformer or spatial processorfollowed by a filter, and for plane wave signals the beamformer iscommon to all and only the filter reflects the particular criterion ofoptimality selected. In all cases the spatial processor or beamformerfunctions to maximize the detectability of deterministic known signalsimmersed in gaussion interference, and it accomplishes this through aset of filter functions which achieve a maximized signal-to-interferencepower density ratio at each frequency. In this sense the beamformer mayproperly be considered a spatial prewhitener; at each frequency itsuppresses peaks in the angular power density function of the noise orinterference.

While optimal processors thus display a commonality of concept and basicfunction, attempts at their implementation have employed a variety ofdifferent approaches and experienced varying degrees of success inachieving optimal processing in practical systems. Many practicalsystems, for example, employ amplitude and phase steering, and arraysthus steered normally are not capable of generating an independentradiation pattern at each frequency as required for the theoreticallyoptimal processor. Another problem arises where the characteristics ofthe useful signal and the noise do not enable temporal discriminationbetween them; in such cases it is difficult to accomplish the desiredprewhitening without suppression of useful signals along with the noise.

Systems affording improved performance capabilities particularly inthese problem areas are disclosed and claimed in the copendingapplication of Dickey et al., Ser. No. 63,113 filed Aug. 12, 1970, whichdescribes an adaptive beamformer with beam mainlobe maintenance.Automatic control of correlation feedback loops in accordance with thepresent invention may advantageously be applied to systems featuringmainlobe maintenance as described in the aforesaid Dickey application,but they are not limited in utility to such systems and have applicationas well to beamformers not incorporating that feature.

SUMMARY OF THE INVENTION The present invention is directed to processorsof the general kind just described and has as its primary ob- 5 jectivethe provision of such optimal processors which achieve desiredperformance even in the presence of large interference transients, andwhich do so in realizable implementations characterized by relativesimplicity and economy of cost.

In its preferred embodiments as herein described the invention utilizesan adaption of a correlation feedback technique which was originallydeveloped for radar sidelobe cancellation. In accordance with theinvention, this technique is applied to provide beamforming and matchedweighting of received signals in an amplitude and phase steered array,through feedback of the beam output signals to correlators at the arrayelements. These correlation feedback loops provide such matchedweighting by nulling or cancelling coherent signals incident upon thearray, except transient signals of low average energy over thecorrelator integration time. Thus the beamformer can receive activepulselike signals with nearly full coherent addition, while suppressingsteady interference.

In certain applications and environments in which interferencetransients are large, however, the signals required to be processed bythe correlation feedback loops may at times become so large as tosaturate them, causing loop instability and consequent impairment ofbeamformer performance continuing until feedback loop stability isrestored. Such problem may be alleviated in accordance with the presentinvention by providing variability of the correlation feedback loop timeconstant, and providing automatic control of this variable by meansresponsive to received signal level so as to hold the loop time constantwithin the range through which correlation loop operation is stable. Inthe preferred embodiment described this time constant control comprisesa sampled-data exponential filter which derives from the array elementalinputs a control signal approximating the average received power, andresponsive to this signal the gain of the correlation feedback loops isadjusted during large input transients as necessary to avoid loopsaturation, while preserving the steady-state performance of thebeamformer essentially unchanged. In other words, the adaptive timeconstant of the system is controlled against dropping below apreselected value which may be specified independently of the steadystate time constant. Use of an exponential filter to provide thiscontrol permits relatively simple implementation and affords a smoothcontrol function which does not disturb the phase behavior of theadaptive process, as would a hard limiting type of control.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of anoptimal array processor of known and generalized form;

FIG. 2 is a block diagram of a processor of the kind to which thepresent invention has primary application; and

FIG. 3 is a block diagram of one implementation of adaptive beam-formerin accordance with the invention.

DETAILED DESCRIPTION With continued reference to the drawings, FIG. 1illustrates an optimal array of elemental and generalized formillustrative of the operation of this general class of processor. Theprocessor as shown may be seen to comprise a combination of twobeamformers, including (1) a primary beamformer which functions totimedelay steer the primary beam to the target position, and (2) aperturbation beamformer which functions to time-delay steer an auxiliarybeam to the interference source. The output of the perturbationbeamformer is passed through a tapped delay line filter 15 which matchesthe frequency response of both beamformers to the incident interference.The beam outputs then are subtracted at 17 to suppress the interference.

The two beamformers in the array processor of Fla? 1 1 both have uniformamplitude, linear phase illuminations, and the array effectivelygenerates a radiation pattern at each frequency which has a null at theangle of the interference. The ability of the optimal beamformer thus togenerate an independent radiation pattern at each frequency offers atheoretical capability of extreme power and flexibility to arrayprocessors of this type.

The realization of this capability is not easily accorn plished,however, in practical systems such as phase and amplitude weightedarrays which must operate across a broad band of frequencies. Suchpractical phased arrays are not capable of generating an independentradiation pattern at each frequency, but rather can generate only asingle radiation pattern which must suffice to suppress broadbandinterference. As a consequence, if a phase and amplitude steered arrayis to succeed in cancelling such broadband interference, the radiationpattern generated by the array must include one or more angularlyextended nulls, to accommodate the apparent spread of radiation evenfrom a point source of broadband interference due to dispersion ofreceptor-to-receptor phase shifts over the frequency band of theinterference.

It is possible to give phase and amplitude weighted arrays thecapability to generate radiation patterns with angulariy extended nulls,and some systems of this kind can perform so well even against broadbandinterference that for many applications of practical interest theperformance degradation normally associated with amplitude and phaseweighting the array signals is not appreciable. As more fully explainedhereinafter, this capability may be achieved by making the signalweighting optimal in the sense that it maximizes the ratio of arrayoutput peak signal to average interference power. By analogy withtemporal processing this optimal illumination function in amplitude andphase steered arrays is referred to as matched weighting, and expressedin the language of matrix algebra it requires that the matrix of inputsignals be multiplied by the product of the inverse of the inputinterference co variance matrix and the matrix of array steeringcoefficients.

In the embodiments of the present invention partieularly describedhereinafter, such matched weighting is achieved in readily andeconomically realizable implementation by use of correlation feedbackloops similar to those employed in radar sidelobe calcellers of the ikind disclosed in [1.8. Pat. No. 3,202,990 to Howells, l and in theco-pending application Ser. No. 165,259, filed Jan. 9, 1962, in thenames of Sidney P. Applebaum, Paul W. Howells and James C. Kovarik, bothpatent and application being assigned to the assignee of the presentinvention.

The cancellers disclosed in these prior cases have found wideapplication in protecting radars against strong noise-like jammingentering through the sidelobes of the antenna response. As fullyexplained in the patent and application, such cancellers employ aplurality of omnidirectional antennas which are disposed in closeproximity to the main dish or array and have a gain roughly equal to thehighest sidelobes of the primary antenna pattern, and which serve assources of amplitude and phase shifted versions of the interferencepresent in the main receiver. The canceller operates through a pluralityof feedback correlation loops 5 to derive amplitude and phaseadjustments to each of the auxiliary channel signals, to combine theadjusted signals to form an auxiliary or perturbation beam, and tosubtract the auxiliary beam signal from the main channel signal. Theautomatically derived amplitude and phase adjustments are such that thesubtraction yields a cancellation of the main channel sidelobe jamming.

One salient characteristic of sidelobe cancellers of this type is thatthe closed-loop time constant of the feedback correlation loops is suchthat the loop lock-on time to low average power waveforms is long,whereas to high average power waveforms it is short. This, in fact, isone means by which the canceller is able to suppress interference butnot useful signal. If the interfer ence in the main channel issufficiently strong to be troublesome even when introduced through thesidelobes, then in the auxiliary channel, with its omnidirectionalsensor, it is quite likely to l() to 30-dh stronger than useful signal.In addition, in most radar applications the useful signal is pulse-likeso that its power, averaged over the closed-loop time constant, is verylow. The interference, on the other hand, is generally a high duty cyclenoise-like wave with a corresponding high power when averaged over theclosed-loop time constant.

The omnis or other auxiliary elements in a multiple sidelobe cancellermay be regarded as elements of an auxiliary array. The amplitude andphase weights derived by the canceller constitute the illuminationfunction for such array. By combining the adjusted auxiliary channelsignals and then subtracting their sum from the main channel signal thecanceller is, in effect, forming an auxiliary or perturbation beam andsubtracting it from the primary beam. Multiple interference sources willbe cancelled provided the perturbation pattern matches the primarypattern at the angles-of-arrival of the interference.

Matched weighting is an application of this multiple sidelobe cancellerprinciple to the phased array. The primary difference associated withthis application is that theomnidirectional elements of the phased arrayserve as sources of both the primary channel signal and the auxiliarychannel signals and no additional sensors are required. FIG. 2illustrates such matched weighting array using feedback correlationloops similar to those of side-lobe cancellers for both beamforming andinterference cancellation. Reference to FIG. 2 indicates that thecomposite receptor signals (1)} are weighted in mixers 19 by a nominalof reference illumination r,,} and summed at 21 to form the referencebeam output:

and also weighted in mixers 23 by a perturbation illumination function{x,, (t)} and summed at 25 to form the perturbation beam output:

N se n ,2, xk (nyku) 2 The net output or resiauabsiasasysaisiaaiarai 27of the perturbation output from the nominal, is then, from equations (1)and (2):

'TZJUT ZTY EGYWY by virtue of equation (3). If it is assumed that thenarrowband filter outputs are slowly varying relative to the channelwaveforms an ensemble average of equation (3 yields:

a v N w) m) G 2 yk( )ym* m m( If it is further assumed that thereceptor-pair correlations of the composite receptor waveforms, y,, *(t)y,,

( t 3, may be approximated by the correlations of just the interference,then equation (5) is equivalent to:

where M is the correlation between the interference at the k" and m"array elements. The validity of this approximation is quite critical,for unless the useful signal correlations may be neglected, the matchedweighting generator will attempt to suppress useful signal as well asinterference.

The net elemental weights, {c (t)}, are given by:

k) "k MU);

Hence, assuming a time invariant reference illumination:

Substitution of equations (7) and (8) into equation (6) yields: M 7

N T Ck'Q) 'i" 6 G 2 Mkm* m( k l, N (9) Having derived a differentialequation specifying each of the N weights, it is now helpful to combinethem into the single matrix equation:

where c the net illumination vector with elements {c (U) c itsderivative M the interference correlation matrix with elements {M r thereference steering vector with elements {r The steady-state solution forthe illumination function is readily seen to be:

and, if the product of the amplifier gain and incident waveform-power ismuch greater than unity, this reducesto: V 1 -1 25s M* l Hence, if thenominal weights are proportional to the useful elemental signals, thederived excitation (to within the error associated with a type zeroservo system) is indeed the desired match weighting.

The transient behavior of the net aperture weights is determined from asolution of the homogenous differential equation:

Unfortunately the solution entails a determination of the eigenvalues of[1+ GIL/1*] which, in general, is quite difficult. However, onesignificant property of the matched weighting generator is easilyestablished. Because the correlation matrix is positive-definite, all ofthe eigenvalues of [l GM*] are necessarily positive and, as aconsequence, the system is unconditionally stable in the sense ofunconditional convergence on the solution.

There are some special situations in which an explicit solution for thetransient response is readily derived. It may be shown, for example,that when the interference is composed of noise (at power level P,,)independent from receptor to receptor, plus narrowband interference (atpower level P,) emanating from a far-field point source, the derivedaperture weights approach their steady state value with the timeconstant:

where T, is the sampling interval and G is the feedback loop gain.Hence, the matched weighting generator locks on rapidly when the productof the number of array receptors and interference power level, i.e., theproduct NP,, is high.

The time constant relation of Equation (l4) may be further simplifiedwhere, as is usually the case, the background signal input into thebeamformer is attributable largely to a directional interference source.In such case the narrowband interference is the predominant input andthe noise input is relatively very much smaller, so that NP, P,,. Thequantity P, may then be neglected, and neglecting also the one whichlikewise is small as compared to NP,, Equation (14) reduces to:

and if time is measured in increments of sample spacing (15) becomes:

In implementing prior canceller and adaptive beamformer systems usingcorrelation feedback loops with N inputs operative in this way, it hasbeen the usual practice in system design to assume a value for theaverage interference power P and then adjust the loop gain G to yield atime constant T sufficiently long to prevent loop response to usefulsignal input. This enables temporal discrimination between useful signaland interference, for cancellation of the latter without also cancellingthe former. Normally the loop time constant is made just sufficientlylong to accomplish this purpose, since to make it any longer would slowthe loop lock on time and reduce cancellation effectivenesscorrespondingly.

Under normal steady-state conditions this design approach has been foundsatisfactory. However, when large interference transients are receivedthe increase in input power P, causes the closed-loop time constant T tobe reduced proportionately, and if the value of this time constant dropsto a point such that it is less than one sample interval, i.e., if T T,or GNP l, the loop becomes unstable. The perturbation beam weights tendto assume very large values and system performance may be seriouslydegraded by undesirable output fluctuations through the duration of thetransient and the recovery period which follows it.

In accordance with the invention, correlation feedback loop stability isassured even in the presence of such large interference transients byaddition of an automatic loop time constant control as illustrated inFIG. 3. Apart from this addition most of the elements in the system ofFIG. 3 are common to that of FIG. 2, carry similar reference numerals,and need not again be described.

The added elements in FIG. 3 include a multiplier 35 which replaces theconstant multiplier G in FIG. 2 and enables adjustment of the feedbacksignal gain in accordance with a control signal input on lead 37. Thisfeedback control signal is generated through a single pole exponentialfilter designated generally by reference numeral 39, from an inputrepresenting the instantaneous received power level averaged over the Nelements of the receptor array. Such average power level signal isderived by processing the received signals through detectors 41 andsumming them at 43, and its gain is adjusted at 45 by a factor la. Thisgain factor is complementary to the gain a of an operational amplifier47 forming part of the filter 39, so as to yield unity gain for thecombination.

Filter 39 functions as a sampled-data exponential filter, and to thisend it comprises a recirculation loop in which a delay element 49 delaysthe recirculating signal through one sampling interval T, beforerecombination with the input in an adder element 51. The filtered outputfrom 39 is a biased and weighted approximation of time-averaged receptorsignal input power, and is applied to one input of a divider 53 whichhas as its other input a fixed reference signal G and which outputs onlead 37 the desired signal for control of correlation loop feedbacksignal gain through mixer 35.

The sampled-data weighting function provided by filter 39, including the1-0: gain factor introduced at 45, may be written as:

where X is the filter input from summer 43 and Y is the output todivider 53. From this relation it will be seen that Y is anapproximation of time-averaged received signal power, and that understeady state conditions the accuracy of this approximation improves as(1 increases to a limit of unity.

Referring again to Equation 16, this relation may be modified to morespecifically describe the operation of filte 39 by replacingJhe gainterm G with the term G which gives:

CI. z o z Here G is a nominal gain constant determined by the value ofthe fixed referenpe signal introduced as one input to divider 53, and Pis the other input thereto representing the approximation which isoutputted by filter 39 of time-average received signal power.

The instantaneous behavior of T may be expressed in terms of thesampled-data weighting function of Equation (17) as follows:

Under steady-state conditions, Y X and the closed-loop time constantbecomes:

TCL N Under worst-case (increasing transient) conditions, Y

X and the time constant decreases to a value of:

TCL 1 a/G N Of interest is the relation between these two time constantvalues.

T (Steady-State)/T (Minimum) 1/1 a,

which is equal to the time constant T,-, of the exponential filter,measured in sample periods.

The operating parameters of the filter may readily be calculated usingEquation (22). If T is the optimized steady-state time constant and T isthe minimum allowable time constant for loop stability, then fromEquation (22) the exponential filter parameter a is seen to be:

a l min/ n and the nominal gain G, is:

G, l/N T The circuitry of FIG. 3 may be simplified in cases where theseveral loop inputs (y,, y y,,) are highly correlated in an envelopesense, i.e., the gross power variations are similar in all loop inputs.In such cases it is possible to use a single loop input y as the signalinput to the exponential filter 39, to thus permit omission of thesumming device 43 and associated circuitry.

Implementation of the exponential filter 39 is feasible in either analogor digital form, though the digital version is the simpler becausecertain of the required signal processing functions, particularly thedelay and division functions, are more easily accomplished with digitalprocessing than with analog. The problems resulting from correlationloop saturation on large interference transients are somewhat differentin analog and digitally implemented beamformer systems, but automatictime constant control in accordance with the present invention ispalliative of the problems of both and thus advantageous in both.Similarly, the invention has application to adaptive beamformer systemswhich include mainlobe maintenace as described in the aforementionedcopending application of Dickey et al., as well as to systems notincorporating that feature. As also described in the Dickey et al. casethe reference and perturbation beamformers may alternatively be of theform in which each elemental signal is weighted by the differencebetween nominal and perturbation weights and then combined, in lieu ofindependently forming the reference and perturbation beams andsubsequentially combining them as described above.

While in the foregoing description of the invention only certainpresently preferred embodiments have been illustrated and described byway of example,

many modifications will occur to those skilled in the art and ittherefore should be understood that the appended claims are intended tocover all such modifica- 5 tions as fall within the true spirit andscope of the invention.

What is claimed as new and desired to be secured by Letters Patent ofthe United States is:

1. In combination with an array of wave receptors, an adaptive arraybeamformer comprising primary beamformer means for phase and amplitudeweighting the elemental signals of said array with nominal weights so asto form and direct a beam mainlobe to the angle of desired maximumresponse of the array, auxiliary, beamformer means including a pluralityof feedback correlation loops each having as inputs the beamformeroutput and one of said elemental signals and being operative to derivetherefrom a perturbation weight and to output a signal which is phaseand amplitude weighted thereby so as to form and direct a null to theangle of arrival of interference, means for adjusting the correlationfeedback loop time constant, and means responsive to said elementalsignals for controlling said time constant adjustment means so as toavoid loop saturation with large interference transients.

2. An array beamformer as defined in claim 1 wherein said meansresponsive to said elemental signals derives therefrom an averagereceived power level signal, and includes sampled-data exponentialfilter means through which said power level signal is processed tointroduce a weighting function such that said correlation loop timeconstant adjustment means responds to power level transients to adjustsaid time constant to maintain correlation loop stability and does notthus respond to steady state changes in power level.

3. An array beamformer as defined in claim 2 wherein said sampled-dataexponential filter means includes a signal recirculation loop providingdelay equal to the sampling interval and gain such as to yield thedesired weighting function.

4. An array beamformer as defined in claim 3, further including meansfor varying the gain of said control signal to obtain the desired steadystate value of correlation feedback loop time constant.

5. An array beamformer as defined in claim 1 wherein said meansresponsive to said elemental signals for controlling said time constantadjustment means comprises means for deriving from at least one of saidelemental signals a control signal varying with the difference ofinstantaneous and time-averaged power levels thereof, and wherein saidmeans for adjusting the correlation feedback loop time constantcomprises loop gain control means operative to adjust loop gain inresponse to the control signal thus derived.

1. In combination with an array of wave receptors, an adaptive arraybeamformer compRising primary beamformer means for phase and amplitudeweighting the elemental signals of said array with nominal weights so asto form and direct a beam mainlobe to the angle of desired maximumresponse of the array, auxiliary, beamformer means including a pluralityof feedback correlation loops each having as inputs the beamformeroutput and one of said elemental signals and being operative to derivetherefrom a perturbation weight and to output a signal which is phaseand amplitude weighted thereby so as to form and direct a null to theangle of arrival of interference, means for adjusting the correlationfeedback loop time constant, and means responsive to said elementalsignals for controlling said time constant adjustment means so as toavoid loop saturation with large interference transients.
 2. An arraybeamformer as defined in claim 1 wherein said means responsive to saidelemental signals derives therefrom an average received power levelsignal, and includes sampled-data exponential filter means through whichsaid power level signal is processed to introduce a weighting functionsuch that said correlation loop time constant adjustment means respondsto power level transients to adjust said time constant to maintaincorrelation loop stability and does not thus respond to steady statechanges in power level.
 3. An array beamformer as defined in claim 2wherein said sampled-data exponential filter means includes a signalrecirculation loop providing delay equal to the sampling interval andgain such as to yield the desired weighting function.
 4. An arraybeamformer as defined in claim 3, further including means for varyingthe gain of said control signal to obtain the desired steady state valueof correlation feedback loop time constant.
 5. An array beamformer asdefined in claim 1 wherein said means responsive to said elementalsignals for controlling said time constant adjustment means comprisesmeans for deriving from at least one of said elemental signals a controlsignal varying with the difference of instantaneous and time-averagedpower levels thereof, and wherein said means for adjusting thecorrelation feedback loop time constant comprises loop gain controlmeans operative to adjust loop gain in response to the control signalthus derived.